Question

Brenda used a compass and found that side YZ is congruent to side BC and that the measure of angle XZY is the same as the measure of angle ACB in the triangles shown below. Using complete sentences, describe the next steps required to prove that triangle XYZ is congruent to triangle ABC.

Answer 1

couldn't you just say that the markings and measurement are the same?

Answer 2

Sortof, but which ones?
Which theorem will you use? SSS, SAS, ASA, AAS, ., . .

Answer 3

How do you figure that out..

Answer 4

Wait.. I think it's sas

Answer 5

You would have to determine another pair of congruent parts, for SAS, Brenda would have to measure XZ = AC.

Answer 6

I don't understand what you mean?

Answer 7

For SAS (side-angle-side) congruence, you need two sides and the angle between them. Right now you have angle C = angle Z, and side ZY = BC. For SAS, you need another side that is adjacent to the congruent angle.

Answer 8

okay It is SAS but you have to explain how you would use a compass to prove the second pair of sides are congruent right? How would I do that?

Answer 9

It depends how strict you want to be with the rules of formal construction.
If you allow compass-carried distance (which is defensible by Euclid's proposition P.I.2.) then you simply measure the sides using the compass.
Otherwise you'll need to use P.I.1. and P.I.2. to construct the congruent side and show that it superposes.